Hello,

I am new to FCT, just tried to solve model nonlinear hyperbolic equation by Zalesak's method as it described in the textbook by Oran and Boris...

My question is - is the staircase-like solution that resulted with flux function f(u) = cu^2 is inevitable... and what is to do with it.... if the simple answer exists?...

Example can be seen at

http://www.geocities.com/andrei_cher...AGES/test1.gif

(donor cell, higher-order Godunov-like and FCT O(dx2, dt) solutions are shown)

And the URL of the"package" that was used to obtain the plot above is:

http://www.geocities.com/andrei_cher...DES/fct.tar.gz

I will appreciate *any* hints..

Andrei

First URL gives: This page is not available.

And second too

FCT has had a tendency to produce these stair-step structures ever since Jay Boris invented FCT back in the 1970s. It is ironic that the subtitle to the original paper was "A Method That Works." I don't believe that subtitle made it into the J. Comput. Phys. article, if memory serves correctly. These stair-steps are numerical junk, and they are the main reason I personally never use FCT. Zalesak made some big improvements to the method, but he didn't completely fix the problem. Consider finding a cure to be a significant research problem.

I'm reminded of a friend's experience with FCT back in the70's.

He's an astrophysicist with an interest in simulating star atmospheres. He tried FCT in his simulation code and managed to calculate a square star!

Needless to say, he doesn't use FCT anymore either.

Yes, really(((( I don't know what is the problem. Just now I have re-submitted "fct.tar.gz" and now this URL works only sometimes

http://www.geocities.com/andrei_cher...DES/fct.tar.gz

This archive contains "test1.gif" file too.

That is seriously funny!!

But... there are working FCT-like programs, e.g. lcpfct, suitable to get great solutions, such as Riemann problem in 1D.. merely

Actually, the subtitle did make into J. Comput. Phys. The paper has been published with the full title

"Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works." J. Comput. Phys. Vol. 11, 1973, pp 38-69.

I do not know whether or not the title was controversial at that time. However, 24 years later J. Comput. Phys. decided to reprint the article in their 30 years anniversary issue in recognition of the impact the article did (more than 500 references).

J. Comput. Phys. Vol. 135, 1997, pp 172-186

Only very few articles has got this kind of appreciation. The flux corrected methodology originated in this article has been successfully applied in many other numerical methods, e.g. Lax-Wendroff, donor-cell, leap-frog, as well as in finite elements and spectral methods.

The staircase error, called terracing in FCT related literature, occurs mostly if the solution is closed to the steady-state. If FCT transport is applied to the real transient flows it gives excellent results. I have successfully applied FTC to transient flows of gases, compressible liquids of almost zero Mach number, and two-phase flows.